... Conversion Corporation,. 680 Garcia Street, Santa Fe, NM 87505, ... vehicle speed, m/s.
An Advanced Fusion Energy System for OuterPlanet Space Propulsion by Robert W. Bussard, Ph.D., Energy/Matter Conversion Corporation, 680 Garcia Street, Santa Fe, NM 87505, Abstract
LEO
= Low Earth satellite Orbit
Inertialelectrostaticfusion IEF devices using polyhe dral magnetic fields for electrostatic potential well con finement of ions o er lightweight sources of large thermal and electrical power from clean p+11B fusion reactions. Application to direct heating o ers propul sion system thrust/mass ratios 1001000x larger than other advanced concepts in the specific impulse range of 1500 < Isp < 1.2E6 sec. Review of engineering interface limits and constraints of these fusion sources shows that no new and unconventional technologies are needed for their achievement Analysis of an outerplanet mission to Titan Saturn’s large moon with dilutedfusionproduct DFF propellant heating engine systems shows single stage vehicles with payload delivery fractions of 0.140.18 of gross launch mass, with transit times of only 1113 weeks. Economic models of development and de ployment of such vehicles suggest that practical, rapid space flight and colonization could be achieved within present budget limits.
LTO
= Low Titan satellite Orbit
= engine system mass, kg
0
= vehicle gross mass, kg
L
= payload mass, kg
p
= propellant mass, kg
Pf
= gross fusion power, MW
Nomenclature a0
= initial vehicle force acceleration, m/s2
af
= final vehicle force acceleration, m/s2
AU
= astronomical unit, distance from E to Sun
B
= magnetic field strength, Tesla
C0
= total cost over mission life, Y,
E
= Earth
E0
= core energy in IEF system, eV
F
= engine thrust, N
F
= engine system thrust/mass ratio
fL
= payload fraction of gross mass
Ggross
= ratio gross fusion to electric drive power
g0
= acceleration of gravity at Earth’s surface
Isp
= engine system specific impulse, s
P, Pne = net fusion or electric power, MW Sb
= incremental distance traversed over b m
b
= engine thrusting ”burn” time, s
T
= surface of Saturn’s moon, Titan
= vehicle speed, m/s
= gJsp= propellant exhaust speed, m/s c
= “characteristic” velocity of flight, m/s
Y
= mission time, years
Introduction Practical space flight requires rapid transits and high payload fractions in singlestage vehicles. This is possi ble only with propulsion systems of very large specific impulse Isp and high engine system thrusttomass ratio F. With high F, gravity “losses” in gfieldclimbing will be minimal; with concurrent high Isp very high char acteristic velocities Vc needed for rapid transits can be achieved as well 1,2. The energy available from chemical reactions limits rocket payload fractions fL to small val ues for most interesting space missions, even with mul tiple staging. And no chemical vehicle system is capable of rapid e.g. less than one year interplanetary flight. The engines needed must have superenergetic perform ance and no massive structures. Nuclear fissio propul sion systems can not meet these requirements3,4. These can be achieved only with nonradiative nuclear fusio reactions that do not require massive shielding, and that yield only energetic charged particles
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The reaction of interest is that between p 1H and 11B. These can be “burned” in special inertialelectrostatic fusion IEF devices 5,6 which trap energetic electrons in quasispherical polyhedral magnetic fields to produce a negative potential well that confines the fusion ions. Such IEF power sources yield energetic MeV charged fusion products alpha particles. These can be trapped in toroidal magnetic fields around the source, and made to heat a propellantdiluent by interparticle collision. Such a dilutedfusionproduct DFP engine system avoids the diculties and thermal limitations of energy conversion and allows attainment of extremely high spe cific impulse 5E41.2E6 sec, best suited for outer planet missions in the solar system. The variation of Isp with F is shown in Figure 1, for these and other concepts of “advanced” fusion propulsion7 , including directelectric quietelectricdischarge QED engines based on IEF use. Details of these other engine systems, their compo nents and subsystems, layout, mass breakdown and per formance have been given in previous studies8,9 ,10.
Specific Impulse, Isp (sec)
107 10
6
Pl
105 104 103
Fu
as
m
el
a
D FP
M
as
s-
A
ug
te Magnetic d Th Fusion Systems er m
Cusp B Fields
Ion Gun
Electron Gun
Injection at Low Ei
Injection at High E0
A
RC
al
10
EXL - Electron Acceleration
QED Fusion Engine Systems
R
en
The IEF fusionelectric source systems of interest here all use quasisphericallysymmetric polyhedral magnetic fields to confine electrons which are injected at high energy Eo, so as to form a negative electric potential well that can confine fusion ions in sphericallyconverging flow. Figure 2 shows a schematic diagram of this electronacceleration EXL IEF system. Fusion ions are inserted into the well near its boundary R, so that they “fall” towards the center and oscillate across the ma chine, with density increasing rapidly 1/r2 towards the center. Typical ion convergence ratios = rc/R are 0.001 < 3 4He, with energy release of 8.68 MeV split between the three alpha particles that are the fusion products fp. The direct production of electric power from these reactions is possible by deceleration of the charged fp ions in an externallyimposed electric field. They will move predominantly radially from their
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central birth point in the IEF core region, and can be collected as they approach zero kinetic energy, by grids or plates placed at appropriate radial positions along the particle path. These collectors are connected to the electrical circuit in which current is driven through the system external load, and are biased so as to slow down the alphas and convert their kinetic energy into electri cal energy in the external circuit. The fusion products of p + 11B have one alpha with a fixed energy of 3.76 MeV and the other two with an energy spread from 74 keV to 4.846 MeV, peaking strongly around 3.76 MeV. The ac tual voltages across the decelerating grids of the direct convertor system DCS will be less than these values12 because the alphas have a charge of Z = 2, and the escap ing fps give up energy to the confining negative potential well, before reaching the DCS region. Typically this may be 180 keV, which then reduces the actual grid voltage range to 0.44 2.24 MV at the outermost grid/plate. To stay within conservative voltage gradients, a complete p + 11B DCS system needs only about 12 grids over 120 cm outside the IEF region required for the controlled fu sion process, itself. In the DFP engine system, a radial distance of nearly 5 m is available see later discussion so that the intergrid voltage gradients can be kept at a low value of only 3.6 kV/cm.
IEF Vacuum System Operation and Fuel Recycling In conventional applications, IEF sources must be main tained and operated at low background pressure < 1E7 torr by continuous vacuum pumping within the outer shell containing both the IEF reaction region and the external region in which electrons and ions recirculate. This will remove both unburned fuel atoms as well as the fusion products, themselves, which must then be separated for subsequent use.
external mixing region. Vacuum pumping of the limiters will then extract the captured fuel ions now neutral atoms and allow them to be recycled back into the IEF system. Design studies show that this will not im pose a significant power loss on the system by use of this IEF/MG device geometry and limiters.
DFP Engine Systems In the DFP engine application, the IEF magnet coils define the active radial boundary R of the source, and are its main structure. In a truncated cube geometry, the electron injectors are mounted at 1.15 R on radial rods extending in from the DFP engine system external confinement/thrust shell. The IEF magnet coils are held in place by mutual interconnects and are supported from the external shell at opposite polar axis locations, sur rounding the dual polar DCS units. These supporting struts also carry the electric current from the DCS to drive the magnets, and the support cylinders that supply the p11B fuel to neutral gas sources that feed the IEF system. Only a very small fraction of the fusion power need be converted to electricity, thus the DCS needed will occupy only a small solid angle at opposite poles of the IEF device.. For this engine, the gross gain of the fusion power system is in the range of Ggross = 4248, thus the electric drive power needed is less than 2.5 of the fusion power produced. The bulk of the fusion product alphas are used to heat the propellant/diluent directly upon their escape from the IEF region.
However, in the DFP engine concept the fusion prod ucts must escape the IEF source into an external region to heat the propellant/diluent injected into this region, while the unburned fuel ions must be trapped and re turned to the IEF system, to avoid unacceptable fuel losses. System thrust level and specific impulse are de termined by control of the mixture ratio of diluent and fusion product mass flows in this external region. The IEF system is bounded by its magnetic coils, insulated from electron impact losses by their selffields. This “magnetic grid” MG arrangement allows recirculation of electrons but not ions from the IEF region, into the external propellant diluent mixing region which, itself, is open to space as its main vacuum pumping system. A simple method exists to capture and reuse unburned fuel before it reaches the mixing region, by use of ion absorbing “limiters” placed just inside the IEF outer boundary so as to intercept fuel ions that have been up scattered, which would otherwise leave the IEF for the
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Configuration, Thermal Loads and Performance The general arrangement of the IEF unit, the DCS and the external confinement/thrust shell in the DFP engine is shown in Figure 3. ÿ ÿ ÿ ÿ ÿ ÿ
$!
%
ÿ ÿÿ #"
ÿ !ÿÿ ÿ ÿ ÿ !ÿ "
#
"
ÿ ÿ &'ÿ
Figure 3 — Schematic Outline of DFP Engine, Showing IEF Placement, Confinement / Thrust Shell, and Magnetic Diverter Exhaust “Nozzle” — Thrust is to the Right
The only unavoidable waste heat that must be removed is that from the magnet coil containers, the electron injection guns, the DCS decelerating grids, and the ex ternal thrust shell that “sees” bremsstrahlung from core electrons. The main thermal power load on the magnets, the eguns, and the DCS grids is that from impact by escaping fusion product ions. Core bremsstrahlung is very much less than the power load from these fusion products. The DCS heating is limited to fusion product ions with residual energy left aer direct conversion has taken place. Detailed analyses have been made11,12 of all the relevant thermal loads on each of the DFP engine system struc tures. These were based on IEF fusion output perform ance derived from complex computer calculations made using the newlydeveloped power balance code, QBAL, a MGinclusive derivative of the earlier PBAL code, which was limited to WieBall loss estimation with MG transport losses ignored. Heat loads and output performance were determined from design studies of the gross fusion power, net power output, gain, drive power, bremsstrahlung, and MG transport loss power required for a range of IEF sources for DFP engine sys tems. Design studies for DFF engine systems used an IEF source with a fusionionconfining radius of R = 5.0m, driven by electron injection at 220 KeV and operated with an ion convergence ratio of = 1E3 with a B field of 13.5 kG at R provided by superconducting mag nets. For these design parameters, the IEF device would yield gross fusion power of Pfus = 10,245 MW with a gross power gain Pfus/Pdriv of Ggr = 46.3. This gives an elec
tron drive power the sum of egun injector losses, bremsstrahlung and MG transport losses of Pdriv = 221 MWe. Assume that the grid structures of the DCS sub tend 0.05 of the DCS surface as viewed from the IEF core, and allow 70 KeV spread in the convertor decel eration process for a deceleration conversion eciency of 0.95. Then, the complete conversion eciency of the DCS will be 0.90. The remaining 0.10 of unconverted power into the DCS must be radiated as waste heat. Since 221 MWe is needed to drive the machine, the DeS must accept a fusion power of 245 MWfus For use of dual, oppositely mounted DCS systems, this requires a DCS acceptance solid angle fraction of 0.012, which is obtained through a 2.19 m radius hole at the external shell radius at 10 m from the IEF core center. The total waste heat load is also this 245 MWth drive and DCS waste heat, which must be dumped to space through a waste heat radiator With full waste heat space radiation, system perform ance is limited only by the maximum propellant specific impulse of fusion product alpha particles from p11B fu sion. These leave with speeds of 2.22.7E9 cm/sec for a particleweighted average speed of 2 .4E9 cm/sec 0. 08c. Averaging over an angular distribution characteris tic of a diuse emitter, the average eective specific im pulse of the propellant/diluent would be Isp = 1.2E6 sec. Lower Isp results from mixing fusion alphas with diluent atoms/ions. The net eective Isp of the mixture is given simply by Ispmix = Isp0/ 1 + D0.5 where Isp0 is the undiluted specific impulse 1.2E6 sec, above and D is the diluent mass flow ratio. For example, if the diluent mass flow rate is taken as three times that of the fusion fuels, then the resulting specific impulse will be onehalf of Isp0. At large dilution ratios the Isp varies as 1/D0.5, so that 10,000:1 dilution yields Ispmix = 12,000 sec.
Subsystems Required The thrust/mass ratio attainable in the DFP system is determined by the masses of all of the subsystems of the complete engine system. First of these is the EXL/IEF unit, consisting of the magnet coils, eguns and power supplies, cryogenic cooling and limiter vacuum systems, fuel feeds, and support structures. These must be driven by electrical power provided by the DCS, which includes the grids and stando structures, and current leads to the IEF loads eguns and magnets. The propulsion thrust subsystem is based on the external to the IEF unit plasma confinement/thrust shell. This is toroidal, with superconducting current carriers to provide the toroidal field that confines the diluent ions and fusion products until they reach some measure of energy equilibration. It also includes the propellant/diluent feed system and pumps and associated support structures. Finally, the mass of the waste heat radiator must be in cluded. Figure 3, previously, gives the arrangement of
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subsystems in the DFP engine, and Figure 4 shows the current paths and resulting B field distributions in the engine system external to the IEF unit.
IEF Unit and Toroidal Confinement Shell The mass of the IEF unit is determined by its magnet coils at radius R. Other masses of note are those of the eguns, ion supplies, and support structures to hold the unit in place within the external shell. The magnet mass is determined by its volume, and this is set by the cross section required for the current for the B fields. In turn, this depends on the current density Ka, amps/cm2 that can be used by the cpo; superconductors. For coils at Ka = 50 kA/cm2 with B field of 13.5 kG, as before, the coil mass is 22,230 kg on a radius of R = 5m. The coil current is 15.3 MA 1.53E7 amps. The external thrust shell, which is spherical, embodies two structures; the superconductors that carry current to generate the outer section of the toroidal magnetic field, and a thin, spherical skin of highstrength steel to carry the magnetic pressure load of these conductors. The fields insulate the shell from impact by the fusion products and heated propellant/diluent ions. The DFP system used 360 conductors running longitudinally on the outside of the steel shell, each carrying 42.5 kA and contained in cryogenically cooled steel tubes. These su perconductors converge as they approach the torus axis, and close the current loop through paraxial conically arranged conductors that connect from the shell surface radius to the IEF main coil feed system, through the DCS structure. These conical conductor sets one at each end of the torus axis support the IEF and bound the DCS volume at each end of this support system. The total mass of the conductors on the shell and return cones exclusive of IEF coils is 11,470 kg. Designing the electrical/magnetic system so that the same current is used for both the IEF B field coils and the shell superconductors gives a B field at the mean shell radius of about 8.2 kG, and a surface field of 4.1 kG. The gyro radius of fusion alphas is only about 12.2 cm at this shell mean radial field. Thus, the IEFtoshell spac ing is ca 41 gyro radii at fusion energies, allowing about 1700 eective energy exchange collisions before permit ting alphas to reach the wall; far greater collisionality than needed to equilibrate the alphas with the propel lant. Figure 4 shows the arrangement of current paths and resulting B fields.
is formed by external field coils that create a “bundle divertor” for confined plasma13 Gross, 1984. Mass flow from this exit hole is the product of plasma density ni at the exit surface, the ion mass i, the exit speed 0.707 i, and the hole area Aex. Multiplying this by the aver age exit speed yields the system thrust, and the thrust times the speed is just the system power. Finally the re lationship between exit plasma density and the toroidal B field is found from the pressure balance p = nE = B2/ 8, where is the plasma “beta” parameter the ratio of kinetic to magnetic pressure at the exit plane.
Current Flow and Toroidal B Field
!
ÿ
ÿ(ÿ ÿ)ÿ ÿÿ * Figure 4 — DFP Engine Current and B Field Configuration
Combining all of these yields an equation for the size of exit hole required as a function of system power, fusion alpha particle energy, diluent mass flow mixture ratio D, plasma , and the surface B field Bex. This equation incorporates all of the relevant physics inter relationships of the system and is:
Aex 1.04
D Pfus E Bex2 1
Here the area is given in cm2 if E is alpha energy in MeV, Pfus is in MW, and Bex is in kG kilogauss. As an example, consider a system with Pfus = 10,000 MW, E = 4 MeV, with D = 25 and a plasma beta of = 0.03 typi cal. For these parameters the exit hole “nozzle” escape area will be Aex = 0.867E6/Bex2 cm2. If Bex = 4.1 kG, as for the current flow conditions used above, this gives Aex = 5.156E4 cm2, for a hole radius of about 128.1 cm., as shown in Figure 3.
Plasma Exhaust Flow and Engine Thrust Propellant exhaust is ejected from the thrust shell through an exit hole on the shell equator. This “nozzle”
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Electrical Power Supply and IEF System Mounting The DCS mass is small because it is converting only about 2.4 of the total system power. With dual axial mounting, the acceptance hole area needed is 1.1 m in radius at the IEF boundary, and the stando distance for the convertor grids can be less than 5 m. The shell return current conductors carry the full magnet drive current through a conical conductor arrangement, delivering current to the distribution coil that feeds the main IEF coils. A similar arrangement takes the current out of the IEF magnets at the opposite end and returns it to the shell conductors. The IEF device is mounted so as to present a triangular face to the DCS units. This face area is about 6 of the total sphere area, thus each DCS free flow area fits well within the small dimensions of these triangular polyhedral faces. The IEF unit, itself, is sup ported from the edge of the DCS hole by the return current conductors, each carrying current to the eguns and to the main coils from the electric power system supplied by the DCS. Three additional structural col umns carry the p11B fuel gas as diborane, B2H6 to the gas injection system that fuels the unit.. Other supports are associated with the placement of the eguns on each of the main square faces. These are mounted on radial spokes extending from the surface shell support struc ture. Estimates give 2290 kg for the mass of the com plete electric system, including dual power conditioning and DCS structures.
with the main space radiators, above, the cryogenic sys tem radiators will have about 800 kg mass. The cryo genic pump mass is estimated to be 1600 kg, and its power supply is taken at 0.5 kg/kWe as 1750 kg, for a cryogenic system hardware mass of about 4150 kg. The complete system must also include fluids stored and used over its life; this is estimated to be about 350 kg, for a total mass of 4500 kg. Other masses include the six eguns, estimated at 840 kg; the propellant/diluent LH2 supply pump system estimated at 500 kg; and the p11B fueling system, includ ing pumps, ion guns/injectors, and limiters, taken as 1000 kg. These and all the other system masses are summarized in Table 1.
Table 1 — System/Subsystem Masses for DFP Fusion Rocket Propulsion Engine Estimated Mass
Comment
Radiator, rad
5,290 kg
3 kg/m2; 1050 K
Misc., misc
1,320 kg
Cryo. cooling system, cryo
4,500 kg
70W/cryoW
Shell, sh
2,950 kg
4.1 kG B fld
Engine S/C, sc
11,470 kg
At 50 kA/cm2
A space radiator capable of handling 245 MW of radi ated power is required to dispose of the 221 MW of elec trical drive power and 24 Mw of unconverted particle power in the DCS. Since the radiator mass is just the product of its area Arad and its specific area density Prad, its mass is fixed by the choice of radiating temperature, for any given emissivity. Using the usual radiation formu las Prad = Trad4, where is the StefanBoltzmann radia tion constant 5.67E12 w/cm2K4, and a specific mass of 3 kg/m2 singlesided while allowing doublesided radia tion, and taking a radiator temperature of 1050 oK, the radiator mass of the example DFP engine system is found to be only 5290 kg.
IEF B field coils, ief
22,230 kg
At 50 kA/cm2
Fusion fuel sys tem, pB
1,000 kg
Diluent system, LH
500 kg
Electric power system, elec
2,290 kg
Similarly, taking 70 watts of electric drive power as re quired for each watt of cryogenic cooling power, and limiting this to the unavoidable minimum due to gamma and Xray heating of the superconductor coils and conductors, it is found that the total cryogenic heat load is about 50 kWth. For this, the cryogenic system drive power must be about 3.5 MWe, all of which must be dumped to space via a radiator system. By analogy
Total, =dfp
Waste Heat Radiator and Cryogenic Cooling System
Subsystem
eguns, eg
840 kg
At 10 kg/MWe 6 @ 140 kg
52,390 kg
Vehicle Flight Performance Practical construction of a singlestage space vehicle requires that its dry mass be at least as large as about 1/e of its full mass. Such a vehicle will give a characteristic
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velocity change increment during powered flight of c = gIsp. Larger total flight velocity increment can be achieved only by use of: a Successive stages, each providing another c from its own propulsive action, or b Vehicles built with considerably less sturdy structure, i.e. with much less than 1/e as dry mass fraction. But: a Multistage vehicles compound the overall ve hicle system massratio in an exponential fash ion. Thus, systems beyond one stage rapidly become unattractive due to the extreme mass growth required to attain flight speeds mark edly in excess of the “characteristic” speed set by gIsp. And, b Systems with flimsy construction are prone to failure and are unreliable, and are therefore un attractive for human space flight. For these reasons, interest here is restricted to single stage, 1/e vehicles only. This limits flight to missions that can be accomplished within the range of c = gIsp values attainable with the DFP engine.
DFP Engine System Specific Impulse As discussed previously, the maximum Isp possible from the DFP engine is about 1.2E6 sec for expulsion of the fusion product alphas, alone, with a sine2 angular distri bution at the engine diverter exhaust plane. A lower limit also exists, set by the maximum plasma density that can be sustained within the confinement/thrust shell with tractable engine B fields and maximum allow able plasma densities external to the IEF unit. This is about at a dilution ratio of D = 200 or so; larger dilution gives higher thrust and lower Isp but may begin to aect IEF operation. Thus the useful and interesting range of dilution ratios in the DFP engine is 1 < D < 200. For the range of D just given, the resulting range of Isp is 1.2E6 > Isp > 7E4 sec, thus the corresponding range of useful singlestage mission flight velocities is 1.2E9 > c > 7E7 cm/sec or from 70012,000 km/sec. Since one Astro nomical Unit AU is about 1.5E13 cm and there are 3.15E7 seconds/year, this velocity range is equivalent to a speed of 1472520 AU/year. It is clear from this that the DFP engine oers promise for both rapid transit mis sions to the Outer Planets OP and for distant sub stellar missions.
constant at its maximum value in any optimum opera tion. Furthermore, although minimum time trajectories may be constructed with variable Isp and constant power, it is always found that maximum payload or dry mass fraction is attained, for any given flight speed increment, by use of maximum Isp throughou the flight. Flight times with these engines are so short, for all missions of inter est, that minimizing flight time is not of most impor tance. Rather, it is important to maximize payload capacity/fraction. Thus, flight analyses can be made on the basis of fixed power and fixed specific impulse. For these conditions, propellant consumption rate and en gine thrust are fixed throughout the flight. Assuming that the flight profile is in fieldfree space then allows ready integration of Newton’s equations for particle mo tion under constant force with changing acceleration. For a rocket vehicle with propellant mass fraction p/ o equal to 1 1/e = 0.632 at start of flight, the vehicle final speed or characteristic velocity increment will be gIsp = , the exhaust velocity of the propellant. Given fixed engine power and constant Isp, the flight time dur ing engine operation will be b = gIsp/a0p/o = 0.632gIsp/a0, where a0 is the initial force acceleration of the full vehicle. Similarly, flight distance under thrusting power is found to be sb = 2/a012/e = 0.2642/a0. To assess actual performance for any desired Isp it is thus necessary to choose a vehicle initial mass and engine power or ratio of power to mass; noting that a0 = 2Pfus/ 0g2Isp. For illustrative purposes take Pfus = 10,000 MW, as previously discussed for the example DFP p11B engine system burns 0.144 gm/sec of p11B, and assume that 0 = 400,000 kg. Then flight performance for various Isp values will be as shown in Table 2, following.
Continuously Accelerating Flight The performance of DFP flight systems can be analyzed simply, by noting that the engine system power will be
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Table 2 — Summary of Accelerating QIS Flights with DFP Engines Parameter
Vallue
Units
All Flightt Profiles Isp
1E+06
3E+05
2E+05
1E+05
D
0.44
15.0
35.0
143
F
200
667
1000
2000
a0
0.5
1.667
2.5
5.0
cm/sec2
dp/d
0.2
2.22
5.0
20
gm/sec
181.6
16.35
7.26
1.82
T
fuel
sec
kg
Con ntinuouslyAccele erating Flight Profile b
40.1
3.61
1.605
0.401
year
sb
35,200 .56 LY
951
281.8
35.2
AU
b =
2100
630
420
210
AU/year
gIsp
c/30
3000
2000
1000
km/sec
From this, note how rapidly the flight “burn” time changes with Isp, as does the p11B fuel consumed, and the distance traversed in powered flight. Note, also, that even though this example is only of a singlestage 1/e vehicle, the highest Isp version is nearly but not quite a starship, covering a distance of 0.56 lightyears LY in its thrusting time of 40.1 years. This really astonishing per formance is a direct result of the extremely high power/ mass ratio of the DFP engine, and of its use of fusion products to provide thrust through the medium of the toroidalfield constrained thrust shell of the DFP sys tem. However, the vehicles in these examples are mov ing at maximum speed at propellant burnout, thus they are impractical for flights involving human crews or sci entific payloads for emplacement at distant points.
Acceleration / Coast / Deceleration Flight Of greater interest are missions in which the vehicle is accelerated to half of its total velocity increment capa bility, coasts a portion of the flight distance, and then decelerates to zero spaceframe speed once again, so that its payloads can be disembarked at a prechosen point in space. Analysis of such acceleration / coast /
deceleration flights is somewhat more tedious than for the simple acceleration profiles of Table 2, but still straightforward because of the unique optimal opera tional conditions for the DFP engine. Following the previous arguments, integration of Newton’s force equa tions gives simple formulas for flight time and distance during the acceleration and deceleration phases of flight. These are: Acceleration
sb1 = 0.0902 2/ a0
b1 = 0.3935 /a0
Flight
pl = 0.3935 0
bl = 0.6065 o
Coast
v gI sp vcoast e 2 2
2
Deceleration
sb2 = 0.06465 2/ a0
b2 = 0.2387 / a0
Flight
p2 = 0.2387 0
b2 = 0.3678 0
Using these formulae, flight performance can be as sessed for any mission distance and any given choice of specific impulse. Note that, for any possible mission
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there will always be an optimum Isp which will give the least transit time This can be found only by use of the formulae, above, for the specified mission. For example, earlier studies showed10 that flight to 557.4 AU the Oort cloud could be accomplished in a minimum time of about 3.3 years at an Isp of approximately 2E5 sec. This vehicle system had a dilution ratio of D = 35.0, thus its propellant mass was largely diluent hydrogen, water, or ammonia, and its structure mass principally that of propellant tankage. With the small vehicle accelerations used 0.01g = 10 cm/sec2, or so, this was assumed con servatively to be 10 of the propellant mass. Then the mass distribution of this example vehicle system was 0 = 400,000 kg as gross mass, propellant mass was p = 252,800 kg, of which pB = 7,260 kg was p11B fusion fuel and H = 245,240 kg was propellant/diluent. Tankage and associated structure was found to be str = 25,280 kg, = 51,705 kg was DFP engine mass, leaving L = 70,215 kg, or 17.6 for payload, guidance, electronics, instruments, etc. This is a very high payload fraction for a singlestage vehicle on such a mission, and illustrates the very great potential of the DFP engine.
Titan Colony Mission An example mission of much greater illustrative value for nearterm use of the DFP engine system, is that of travel to and colonization of Titan, the largest moon of Saturn. This body is believed to have ice and thus wa ter on its surface; it is larger than Earth’s moon, and has a larger surface gravity, being about 1/5 that of Earth. It is su ciently far from Saturn that its orbit is not pro hibitively deep into Saturn’s gravitational well. Thus it is accessible to ultrafast deepspace vehicles with high deltavee capabilities, without significant propulsion and payload penalties. However, in order to accomplish such a colonization mission over a reasonable period of time e.g. ten years the vehicle propulsion system used must be able to provide transit times measured in tens of days, rather than in tens of years.
Mission Characteristics The orbit of Saturn varies from 910 AU from the Sun, thus its distance from the Earth may vary from 811 AU, depending on whether it is in opposition or conjunction with the Earth. Averag flight speeds needed are then in the range of 10 AU per 100 days, or 15 Mkm/day or 200 km/sec, for example. Such average speeds imply four times this for vehicle characteristic velocity for an accelerationcoastdeceleration flight profile, thus vehi cle characteristic velocity capability must be in the range of Vc = 800 km/sec, or Isp = 80,000 sec, a truly stunning value by present standards. Using the Newtonian formu lae just given, the Isp required for nocoas flight to Titan ranges from 72,500 sec to 80,700 sec for transits over
8.0 AU closest approach to 11.0 AUmost distant path. A specific impulse value of Isp = 70,000 sec was used for the analysis, thus all mission flight profiles had mid course coas flight segments. The Earth to Titan transfer vehicle using this DFP en gine would leave from LEO and travel to a low orbit about Titan LTO. Its thrust is too small to allow direct surface landing; thus some form of LTO/T shuttle is required to o oad passengers and payload to the Titan surface. However, the low surface gravity of Titan allows a T/LTO shuttle of only modest capability, as com pared to that required for E/LEO, for example. The LEO/L TO transfer vehicle loaded gross mass in LEO is taken to be 400 T 11, with an engine system mass of 52 T as above, 252 T of propellant, 25 T for fixed crew and habitat quarters and associated life support systems, and 26 T for structure propellant tankage, etc. The remain der is useful payload of 45 T. The vehicle outline is shown in the sketch given in Figure 5, following:
#ÿ * ÿ $!
7#ÿ
+, ÿ-&./01ÿ ,ÿ 2 & ÿ(ÿ3 / ÿ ÿ 4 ÿ ÿ 1 ÿ ÿ " 5+ 5ÿ, 5ÿ6 ÿ 5ÿ$ ÿ 5ÿ(( ÿ
4ÿÿ ÿ !ÿ ÿÿ ÿ,
Figure 5 — Schematic Outline of LEO/LTO Transfer Vehicle
With these masses, the vehicle speed at the end of the initial thrusting phase is found to be 343.2 km/sec, or 0.2 AU/day. Additional vehicle energy required for capture into Titan’s orbit around Saturn and into low orbit around Titan must be added at this point in the flight. Since escape from Saturn at Titan’s orbital distance re quires 8077 m/sec and escape from Titan’s surface needs 2990 m/sec, the total velocity increment needed at Titan is 11,067 m/sec, or about 11.1 km/sec. Because of the very high speed at midcourse of 343.2 km/sec, the energy addition can be made here with a velocity increment of 343.22+11.120·5 = 173 m/sec; which requires about 125 kg of additional propellant. This is trivial and ignorable as compared to the rest of the flight requirement.
Mission Parameters and Economics Estimates For this mission, it was assumed that an onground col ony of 400 people would be established on Titan over a period of 10 years, with recycle rotation back to Earth allowed for each colonist, once every year. With the
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chosen specific impulse, the transit times for E/T flight are in the range of 75 to 90 days, or 2.53 months for each OW trip. Personnel recycle then requires 56 months, and LEO/LTO vehicle flight usage can not practically exceed 1.5 RT per year. Allowing 6 months on Earth for rotational leave then gives only a 50 duty factor for Titanbased personnel. With this assumption 400 people must be in transit or on Earth at any one time aer establishment of the 400 person onground Titan colony. While the colony is be ing established the personnel interplanetary transfer rate is about twice the onground population count, but the transport rate of capital plant and equipment to set up the colony is just that required for the 400 colony sta personnel on the ground. For cost estimation, it was assumed that 60 T of capital plant and equipment, and an expendable mass of 2000 kg/person is carried on each transfer flight. E/LEO transport costs are taken at 27.0/kg, from earlier studies, and 24.2/kg is allowed for low Titan satellite orbit to ground LTO/T transport delivery. The dominant cost is that of LEO/LTO trans port; this has been estimated at 280/kg, excluding any financial costs, but with operations and maintenance O&M costs taken at 2 per flight over 100 flights per vehicle. These economic and cost assumptions and con ditions have been discussed in more detail previ ously8,11,12. Under these conditions the total cost rate for this mission becomes:
dC0 1.235 x10 9 0.772 x10 8 ÿÿÿY ($ / year ) dY
cost less than 1/3 of the NASA annual budget over this time. Once established these could become self supporting and engage in expansion of their own, again using DFP engine systems. The value of such colonies is almost impossible to quan tify at present. The only model available for such guesstimates is that facing Columbus when he first set sail for what was to prove to be North America. History has shown that the visions of his sponsors and contem poraries were woefully inadequate to project the future value of the civilizations, industries, knowledge and ideas that would grow in this new environment. Would space colonization be expected to be any less important or valuable? The DFP engine systems oer almost the only means presently seen to carry out such ventures. Their development and use will give us the tools to find the answers to these questions, which can be found only by human expansion into the interplanetary frontiers of our Solar System.
Revision History Copyright 2001 by Robert W. Bussard. Published by permission by the American Institute of Physics AIP Conference Proceedings January 14, 2002 Volume 608, pp. 768779, Space Technology and Applications International Forum. Reformatted and color illustrations added August 2007 by Mark Duncan. References updated April 2009.
3 from which the integrated cost over the desired Y = 10 year period is found to be Co10 = 16.21E9 = 16.21B for OW delivery of a 400 person colony to Titan, with 24,000 metric T of capital plant together with support ing facilities. housing, life support, medical, communica tions, et al, and transfer vehicle maintenance and refuel ing equipment. True roundtrip costing requires knowl edge of market value on Earth of material transported back from Titan, or from other points in the outer solar system. Certainly such vehicles could be used to mine the asteroids, to move small asteroids, establish colonies on the moons of Jupiter, etc, whose potential future value is yet di cult to estimate.
Summary and Conclusions Previous studies of DFP engine system performance have analyzed two other Colony mission; one to put 4000 people on the Moon, and another to establish 1200 people on Mars, each with 25 to 50 T per person, respectively, of installed infrastructure. Total costs of these three Colony missions were found to be about 45 B for their completion over a ten year period, for a total
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References 1
Robert W. Bussard and Richard D. DeLauer; Nuclear Rocket Propulsio, McGrawHill Book Co., NY, 1958. 2
Maxwell Hunter; “Solar System Spaceships,” Thrus Into Spac, Holt, Rhinehart & Winston, NY, 1966, Chapter 5.
3
Robert W. Bussard and Richard D. DeLauer; Funda mentals of Nuclear Fligh, McGrawHill Book Co., NY, 1965.
4
Robert W. Bussard; “ASPENIT: TwoStaging and Ra diation Shielding Eects On ASPEN Vehicle Perform ance,” LA2680, 6nS/62, declassified with deletions 9/6/ 1967; and in “ASPEN: Nuclear Propulsion for Earthto Orbit Aerospace Plane Vehicles,” RW. Bussard, Proceed ings International Conference on Spacefligh, Rome, June 1971.
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Robert W. Bussard; “System Technical and Economic Features of QEDengineDriven Space Transportation,” AJAA973071, paper given at 33rd AIAA/SAE/ASME/ ASEE Joint Propulsion Conferenc, Seattle, WA, 69 July 1997. 12
Robert W. Bussard and H.D. Froning; “System/ SubSystem Engineering Interface Considerations and R&D Requirements for IEF /QEDd Engine Systems,” Paper #232, Section F, STAlF98, 15th Proceedings of Space Technology and Applications International Foru, Al buquerque, NM, 2529 January 1998. 13
Robert A. Gross; “Fusion Energy,” John Wiley & Sons, Inc., NY, 1984, p. 134 .
5
Robert W. Bussard; “Method and Apparatus For Con trolling Charged Particles,” U.S. Pat 4,826,626, 5/2/1989, and “Physics Considerations of MagneticInertial Electrostatic Confinement A New Concept for Spheri cal ConvergingFlow Fusion, Fusion Technology, v19, March 1991, 273. 6
Nicholas A. Krall; “The Polywell: A Spherically Convergent Ion Focus Concept,” Fusion Technology, vol ume 22, August 1992, p. 42. 7
John F. Santarius; “Magnetic Fusion Energy and Space Development,” Proceedings 24th Intersociety Energy Conver sion Conferenc, IEEE, v5, 1989, pp 2525. 8
Robert W. Bussard; “The QED Engine System: Direct Electric FusionPowered Rocket Propulsion Systems,” Paper #263, Proceedings 10th Symposium on Space/Nuclear Power and Propulsio, Albuquerque, NM, 1014 January 1993.
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Robert W. Bussard and Lorin W. Jameson; “The QED Engine Spectrum: FusionElectric Propulsion for Air Breathing to Interstellar Flight,” AIAA paper 932006, 29th Joint Propulsion Conference, Monterey, CA 6/28 30/ 1993; Journal of Propulsion and Power, v11, n2, pp. 365/ 372. 10
Robert W. Bussard, Lorin W. Jameson and H.D. Fron ing, Jr.; “The QED Engine: FusionElectric Propulsion for CisOort/QuasiInterstellar Flight,” Proceedings of th 44th Congress at the International Astronautical Federatio, 10/22/1993, Graz, Austria.
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